Determining Coplanarity of four points

[jrotmensen]

How do you determine Coplanarity of four points?
I am given A(3,1,0), B(2,-3,1), C(-1,0,4), D(5,-6,-2).

Do i make vectors for each point from the origin? (But that wouldn't work would it? :()
Can anybody point me in the right direction?

Thanks!

 

[rock.freak667]

if a,b,c are coplanar vectors then
a.(bxc)=0

 

[jrotmensen]

if a,b,c are coplanar vectors then
a.(bxc)=0

at this point, we haven't learned vector*vector multiplication.
is there any other way?

also, how should i get the vectors? displacement of the point from the origin? or displacement from one point to another??

 

[HallsofIvy]

The equation of any plane (that does not include the origin) can be written in the form Ax+ By+ Cz= 1. Replace x, y, and z by the coordinates of three of your points to get three equations to solve for A, B, and C. (If you can't, it is because the plane includes the origin- so try again with Ax+ By+ Cz= 0.)

Once you have the equation of the plane that contains three of the points, put the coordinates of the fourth point into that equation and see if they also satify the equation.